Symbiosis National Aptitude Test SNAP 2016 Paper

ax + by = 6
⇒ ${\left(\mathit{a}\mathit{x}+\mathit{b}\mathit{y}\right)}^2$ = 36
${\mathit{a}}^2{\mathit{x}}^2+{\mathit{b}}^2{\mathit{y}}^2$ + 2abxy = 36 —— (i)
bx – ay = 2
⇒ ${\left(\mathit{b}\mathit{x}\mathit{–}\mathit{a}\mathit{y}\right)}^2$ = 4
${\mathit{b}}^2{\mathit{x}}^2+{\mathit{a}}^2{\mathit{y}}^2$ – 2abxy = 4 —— (ii)
By equation (i) + equation (ii)
We get, ${\mathit{a}}^2{\mathit{x}}^2+{\mathit{b}}^2{\mathit{y}}^2+{\mathit{b}}^2{\mathit{x}}^2+{\mathit{a}}^2{\mathit{y}}^2$ = 40
$\left({\mathit{a}}^2+{\mathit{b}}^2\right)\left({\mathit{x}}^2+{\mathit{y}}^2\right)$ = 40
$\left({\mathit{a}}^2+{\mathit{b}}^2\right)$ 4 = 40
⇒ ${\mathit{a}}^2+{\mathit{b}}^2$ = 10